A "previous damage" title may be used by some states' DMV (namely Arkansas) and it is similar to what is referred to in most states as a rebuilt or reconstructed motor vehicle title.
A rebuilt or previous damage title in general means the car was in a serious accident or one in which the insurance company declared the car a total loss but then the vehicle was purchased and rebuilt or repaired and was once again found to be street worthy.
A salvage title in some states means the same thing while in other states a salvage title means that the vehicle can be sold for parts but is not street worthy. In some states a car with a salvage title can be repaired and then obtain a rebuilt title from the DMV.
According to information given from the Arkansas DMV the owner of any motor vehicle registered in Arkansas at the time of damage, that has received physical damage equal or exceeding seventy percent (70%) of its average retail value, or water damage to the extent that the vehicle was submerged to any level above the dash board, is required to surrender a completed "Declaration of Damage" and the existing title, and apply for issuance of a "Damaged" branded title.
When such motor vehicle is rebuilt or reconstructed, the owner, and re-builder if he is not the owner, is required to surrender to the AR Department of Finance and Administration a completed copy of this affidavit and the existing "Damaged" branded title, and apply for issuance of a new title bearing the notation "Previous Damage". Motor vehicles registered in Arkansas at the time of damage, which are six (6) years old or older at the time of damage, are exempt from these requirements.
CarFax gives information on types of titles as part of their car history. For Arkansas it states that when a vehicle is submerged above the dashboard or sustains damage of 70% or more of its retail value, Arkansas issues a title branded damaged. When the vehicle is repaired, Arkansas issues a title branded previous damage. Arkansas carries forward brands from other states that are similar to its own on all subsequent titles.
CarFax simplifies this even more by stating that in AR a previous damage title means that the vehicle was damaged and rebuilt and the vehicle's title is now branded by the states as previous damage. While with a salvage title the vehicle was damaged to the extent that repair costs were at least 70 percent of the vehicle's retail value or the vehicle was submerged above the dashboard. The vehicle's actual title was then branded as damaged or salvage.
To find out more about the different branding of titles in your state contact your Department of Motor Vehicles.